Subgraph Entropy
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908418558656512 |
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| author | Aougab, Tarik Clay, Matt Hamed, Tawfiq |
| author_facet | Aougab, Tarik Clay, Matt Hamed, Tawfiq |
| contents | Given $r \geq 3$, we prove that there exists $λ>0$ depending only on $r$ so that if $G$ is a metric graph of rank $r$ with metric entropy $1$, then there exists a proper subgraph $H$ of $G$ with metric entropy at least $λ$. This answers a question of the second two authors together with Rieck. We interpret this as a graph theoretic version of the Bers Lemma from hyperbolic geometry, and explain some connections to the pressure metric on the Culler-Vogtmann Outer Space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_18838 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Subgraph Entropy Aougab, Tarik Clay, Matt Hamed, Tawfiq Geometric Topology Dynamical Systems Given $r \geq 3$, we prove that there exists $λ>0$ depending only on $r$ so that if $G$ is a metric graph of rank $r$ with metric entropy $1$, then there exists a proper subgraph $H$ of $G$ with metric entropy at least $λ$. This answers a question of the second two authors together with Rieck. We interpret this as a graph theoretic version of the Bers Lemma from hyperbolic geometry, and explain some connections to the pressure metric on the Culler-Vogtmann Outer Space. |
| title | Subgraph Entropy |
| topic | Geometric Topology Dynamical Systems |
| url | https://arxiv.org/abs/2506.18838 |